Question

Express the following as a power with the base 4:
$4^3\times 4^{-2}\times {16}^2$

• A. $4^3$
• B. $4^4$
• C. $4^5$
• D. $4^6$

Answer 1

The correct option is C

$4^5$

$4^3\times 4^{-2}\times {16}^2$
$=4^3\times 4^{-2}\times {\left(4^2\right)}^2$
$=4^3\times 4^{-2}\times 4^4$
$[\because (a^m{)}^n=\left(a{)}^{m\times n}\right]$
$=4^{3-2+4}$
$[\because a^m\times a^n=a^{m+n}]$
$=4^5$